ATP holders can instruct, but that doesn't give them examining authority.
For the issuance of an FAA SIC you'd need to log the (authorised) ground and flight training, and visit a FSDO.
Second-In-Command Type Rating | NBAA - National Business Aviation Association
Instead, if it is a piggyback FAA license based on your EASA one, then this process may help.
Airmen Certification ? Administrative Process for the Reissuance of FAA Pilot Certificates